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DO NOW: SET UP CORNELL NOTES

DO NOW: SET UP CORNELL NOTES. Assign yourself. Set up notes for Cornell style. Write down the objective, date, class, etc. Merry Newtonmas … a little Late!. USAIN BOLT AND sir ISAAC NEWTON. Review from limits so far: our methods. FIRST, try plugging in the x-value.

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DO NOW: SET UP CORNELL NOTES

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  1. DO NOW: SET UP CORNELL NOTES • Assign yourself. • Set up notes for Cornell style. • Write down the objective, date, class, etc.

  2. Merry Newtonmas… a little Late!

  3. USAIN BOLT AND sir ISAAC NEWTON

  4. Review from limits so far: our methods • FIRST, try plugging in the x-value. • Use a table on the calculator. Several ways to do this. • Plug the function into Y= • Go to TBLSET (2nd-WINDOW), and set the TblStart to the x value, and the Delta-Tbl to .001 • Write down the Xs and Ys three before and three after your x value. • Use your brain to estimate the one that’s missing in between – if there is no sensible in between (a huge jump), write DNE • Use a graph • Cancel Out Common Factor, Then Plug In Again -> NEW METHOD we are learning today

  5. Limits method #4: canceling Example: • Factor the numerator and denominator. • Cancel any common factors. • Try plugging in the x again.

  6. Rules for limits • Treat composite functions (e.g. f(x) + g(x), f(x) x g(x), etc.) just like regular algebra. • If you are multiplying by a constant, you can factor out the constant. • If you are multiplying two functions, you can multiply their limits. • If you are dividing two functions, you can divide their limits. • Let’s PRACTICE – Half sheet!

  7. Limits to Infinity! • Anything over infinity becomes zero. • Zero over anything (except zero) becomes zero. • But what if we have something to infinity? Like these: • The steps: Divide EVERYTHING by the biggest power of x, then plug in infinity. 

  8. Asymptotes Using Limits • Rational functions have an x in the denominator. • Asymptotes may be vertical, horizontal or oblique. • Oblique means “slant.” We don’t have to know it for IB. If you do need to know it in college, your professor will DEFINITELY teach it again. • Example: Find any asymptotes of the function below and discuss the behavior of f(x) near these asymptotes.

  9. QUIZ TOMORROW: YOU SHOULD KNOW… • Describe what a limit is and why limits are useful. • Name the three methods we can use to find limits and give a brief explanation of how to find it with each method. • (First, try plugging it in. If that works, don’t mess with it anymore.) • Graph • Table • Cancel Common Factors and then plug in • Use a graph to find limits. • Use a table to find limits. • Know when a function does not have a limit (DNE). • Find the slope at one point on a curve using limits. All of this can be found in your Piggy Bank notes except for method #3 which we did today. Limit Rules/Asymptotes are not on it.

  10. Before you start… • Homework Due Tomorrow: • PG 465: Finish #1, #2, #3 (ALL) • PG 467: Finish #1 • You will get your Mock Paper 1s back tomorrow. Corrections are mandatory (not stamped, but graded) and due Monday. Plan ahead.

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